Determine whether the points P(1, 0), Q(2, 1) and R(2, 3) lie outside

1.	Determine whether the points P(1, 0), Q(2, 1) and R(2, 3) lie outside the circle, on the circle or inside the circle x2 + y2 – 4x – 6y + 9 = 0.
Answer» The equation of the circle is x² + y² – 4x – 6y + 9 = 0 PT² = x₁² + y₁²– 4x₁ – 6y₁ + 9 At P(1, 0), PT² = 1 + 0 – 4 – 0 + 9 = 6 > 0 At Q(2, 1), PT² = 4 + 1 – 8 – 6 + 9 = 0 At R(2, 3), PT² = 4 + 9 – 8 – 18 + 9 = -4 < 0 The point P lies outside the circle. The point Q lies on the circle. The point R lies inside the circle.

Determine whether the points P(1, 0), Q(2, 1) and R(2, 3) lie outside the circle, on the circle or inside the circle x2 + y2 – 4x – 6y + 9 = 0.

Answer»

The equation of the circle is x² + y² – 4x – 6y + 9 = 0

PT² = x₁² + y₁²– 4x₁ – 6y₁ + 9

At P(1, 0), PT² = 1 + 0 – 4 – 0 + 9 = 6 > 0

At Q(2, 1), PT² = 4 + 1 – 8 – 6 + 9 = 0

At R(2, 3), PT² = 4 + 9 – 8 – 18 + 9 = -4 < 0

The point P lies outside the circle.

The point Q lies on the circle.

The point R lies inside the circle.